A Leavitt path algebra over a field has a unique isomorphism class of graded-simple left modules precisely when its graph is row-finite, downward directed, and generated by a single line point or an exit-free cycle; then the algebra is graded-isomorphic to a graded matrix algebra over K or…
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Graded Naimark's Problem for Leavitt Path Algebras
A Leavitt path algebra over a field has a unique isomorphism class of graded-simple left modules precisely when its graph is row-finite, downward directed, and generated by a single line point or an exit-free cycle; then the algebra is graded-isomorphic to a graded matrix algebra over K or…